How do I UV unwrap this shape in to one island?
I would mark two seam rings.  One around the outside of the donut, and another cutting across  a small ring of the donut:


The problem is that the quality of the unwrap you get from blender's default logic can be pretty variable.  A plain unwrap sort of pinched the ends of the rectangular island.  The "follow active quads" depends on the state of the uv map when it starts (the screenshot shows one of the less disastrous outcomes).

The best uv unwrap seems to be when you do a Reset (which makes every quad cover the entire image) and then a Follow Active Quads.  Then you can scale it to fit in the image, or leave it huge to tile a texture.